It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random numbers are required to obtain one sample value of the integrand, since those problems are extremely high-dimensional integrations, for example, risk measurement of credit portfolio. This leads to the situation that the required qubit number is too large in the naive implementation where a quantum register is allocated per random number. In this paper, we point out that we can reduce qubits keeping quantum speed up if we perform calculation similar to the classical one, that is, estimate the average of integrand values sampled by a pseudo-random-number generator (PRNG) implemented on a quantum circuit. We present not only the overview of the idea but also concrete implementation of PRNG and application to credit risk measurement. Actually, reduction of qubits is a trade-off against increase of circuit depth. Therefore, full reduction might be impractical, but such a trade-off between speed and memory space will be important in adjustment of calculation setting considering machine specs, if large-scale Monte Carlo simulation by quantum computer is in operation in the future.

Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The $C_6$ and $C_9$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated $C_6$ coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the $C_6$ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the $C_9$ coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., ${\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.

The efficient suppression of autoionizing collisions is a stringent requirement to achieve quantum degeneracy in metastable rare gases. Here, we report on the suppression of Penning ionization in collisions between metastable He and laser-excited Li atoms. Our results show that the suppression is achieved by the conservation of both the total electron spin and $\mathrm{\Lambda }$, i.e., the projection of the total molecular orbital angular momentum along the internuclear axis. Our findings suggest that $\mathrm{\Lambda }$ conservation can be used as a more general means of reaction control, in particular, to improve schemes for the simultaneous laser cooling and trapping of metastable He and alkali-metal atoms.

The periodically modulated Bose-Hubbard dimer model offers an experimentally realizable and highly tunable platform for observing the scrambling of quantum information and the apparent thermalization of isolated, interacting quantum many-body systems. In this work we apply fidelity out-of-time correlators (FOTOCs) to establish connections between the thermalization in the Floquet system, the exponential growth of FOTOCs as quantified by a nonzero quantum Lyapunov exponent, and the underlying classical transition from regular to chaotic dynamics in the dimer. Moreover, we demonstrate that a nonzero quantum Lyapunov exponent can also be inferred from measures quantifying the delocalization of the Floquet modes of the system such as the Shannon entropy, which approaches unity if the system thermalizes to the periodic Gibbs ensemble prediction.

We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.

Spin and orbital angular momenta are separately observable properties of light. Both of them can interact with matter, causing an exchange between each other and generating an optical torque on the matter. However, thus far, we have been unable to separately discuss the transfer of the spin and orbital angular momenta or the origin of the optical torques with regard to them. Here, we consider the optical chirality density and propose an approach to analyzing the transfer of spin and orbital angular momenta separately by considering this property. Our approach is based on a continuity equation for spin angular momentum density. This equation is derived from an extended proportional relation between the chirality flux density and spin angular momentum density in sources-added space. Our findings will greatly facilitate the study of angular momentum interaction between light and matter.

Spatial search by a discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e., in a time that is in the square root of the hitting time of $P$. However, in the framework of continuous-time quantum walks, it was previously unknown whether such general speedup is possible. In fact, in this framework, the widely used quantum algorithm by Childs and Goldstone fails to achieve such a speedup. Furthermore, it is not clear how to apply this algorithm for searching any Markov chain $P$. In this article we aim to reconcile the apparent differences between the running times of spatial search algorithms in these two frameworks. We first present a modified version of the Childs and Goldstone algorithm which can search for a marked element for any ergodic, reversible $P$ by performing a quantum walk on its edges. Although this approach improves the algorithmic running time for several instances, it cannot provide a generic quadratic speedup for any $P$. Second, using the framework of interpolated Markov chains, we provide a spatial search algorithm by a continuous-time quantum walk which can find a marked node on any $P$ in the square root of the classical hitting time. In the scenario where multiple nodes are marked, the algorithmic running time scales as the square root of a quantity known as the extended hitting time. Our results establish a connection between discrete-time and continuous-time quantum walks and can be used to develop a number of Markov chain-based quantum algorithms.

A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multielectron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance.

We study radiative cooling processes of ${\mathrm{N}}_2{\mathrm{O}}^{+}$ ions isolated in vacuum by taking advantage of the extended storage times possible with a cryogenic electrostatic ion storage ring. The temporal evolution of the internal state populations of the ${\mathrm{N}}_2{\mathrm{O}}^{+}$ ions after being stored in the ring was state-selectively measured by action spectroscopy via a predissociation process using a wavelength-tunable pulsed laser. The rotational level population remained unchanged up to about 200 s after ion storage, which is consistent with theoretical predictions and the small permanent dipole moment. On the other hand, we found that depletion of the vibrational excited states in the NN-O stretching mode proceeded within 5 s, while a noticeable increase of the ground-state population was not observed. This implies that the initial populations of the vibrational excited states are relatively small. We discuss such behavior in the context of the initial population distribution of ions extracted from the ion source with a simulation based on simple cascade modeling.

A spin-1 condensate with antiferromagnetic interactions supports nematic spin vortices in the easy-plane polar phase. These vortices have a $2\pi$ winding of the nematic director with a core structure that depends on the quadratic Zeeman energy. We characterize the properties of the nematic spin vortex in a uniform quasi-two-dimensional system. We also obtain the vortex excitation spectrum and use it to quantify its stability against dissociating into two half-quantum vortices, finding a parameter regime where the nematic spin vortex is dynamically stable. These results are supported by full dynamical simulations.

Rotons can exist in ultracold atomic gases either with long-range interactions or with spin-orbit-coupled dispersions. We find that two different kinds of rotons coexist in a joint system combining long-range interactions and spin-orbit coupling. One roton originates from spin-orbit coupling and two others come from long-range interactions. Their softening can be controlled separately. The interesting phenomenon which we find is that spin-orbit-coupled roton can push down the energy of one long-range-interaction roton. The spin-orbit coupling accelerates the softening of this roton. The post phase of spin-orbit-coupling-assisted roton softening and instability is identified as a superstripe.

As the research of topological semimetals develops, semimetals with nodal-line rings have come into people's vision as a new platform for studying electronic topology. We propose a method that uses ultracold atoms in a two-dimensional amplitude-shaken bipartite hexagonal optical lattice to simulate the nodal-line semimetal, which can be achieved in the experiment by attaching one triangular optical lattice to a hexagonal optical lattice and periodically modulating the intensity and position of the triangular lattice. By adjusting the shaking frequency and well depth difference of the hexagonal optical lattice, a transformation from Dirac semimetal to the nodal-line semimetal is observed in our system. This transformation can be demonstrated by the Berry phase and Berry curvature, which guides the measurement. Furthermore, the amplitude shaking and $C_3$ symmetry generate a time-reversal-symmetry-unstable mode, and the proportion of the mode and the trivial mode of the hexagonal lattice controls the transformation. This proposal paves a way to study nodal-line semimetals in two-dimensional systems, and it contributes to the application of nodal-line semimetals.

We study spin-1/2 fermions in spin-dependent potentials under the spin-model approximation, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin-model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long range and spin anisotropic. We consider a Ramsey-type sequence in which quantum degenerate, initially spin-polarized fermions are rotated to a spin superposition, and the differences in potential for the two spin states induce $s$-wave interactions. Applied to such a setup, we show that the spin-model approximation qualitatively captures the collective spin dynamics for weak interactions compared to the harmonic-oscillator frequency, and often captures quantitative features at timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections for both collective spin and fidelity metrics when realistic anharmonic potential corrections are taken into account, demonstrating that anharmonicity can significantly improve the fidelity of the spin-model approximation. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in density-matrix renormalization group analyses, and may have broader applicability within the tensor network community.

A scheme for generating powerful terahertz (THz) radiation based on laser-solid interactions is proposed. When a $p$-polarized femtosecond laser impinges obliquely on a plane solid target and the target partially blocks the laser energy, surface electrons are extracted to the vacuum and accelerated by the laser fields, forming a low-divergence electron beam. A half-cycle THz radiation pulse is emitted simultaneously as the beam passes by the edge of the target, due to a mechanism similar to coherent transition radiation. Our particle-in-cell simulations show that a relativistic THz pulse can be obtained with an energy of a few tens of millijoule and a conversion efficiency above $1\%$, with existing joule level femtosecond laser sources.

This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free-space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave, and acoustic waves.

The Dicke model, which describes the dipolar coupling between $N$ two-level atoms and a quantized electromagnetic field, seemingly violates gauge invariance in the presence of ultrastrong light-matter coupling, a regime that is now experimentally accessible in many physical systems. Specifically, it has been shown that, while the two-level approximation can work well in the dipole gauge, the Coulomb gauge fails to provide the correct spectra in the ultrastrong coupling regime. Here we show that, taking into account the nonlocality of the atomic potential induced by the two-level approximation, gauge invariance is fully restored for arbitrary interaction strengths, even in the $N\to \infty$ limit. Finally, we express the Hopfield model, a general description based on the quantization of a linear dielectric medium, in a manifestly gauge-invariant form, and show that the Dicke model in the dilute regime can be regarded as a particular case of the more general Hopfield model.

We demonstrate 1D simultaneous laser cooling of ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms using an optical frequency comb. By adjusting the pulse repetition frequency and the offset frequency, the frequency comb spectrum is tuned to ensure that two distinct frequency comb modes are simultaneously red-detuned from the cooling transitions, one mode for each species. Starting from a precooled cloud of ${}^{85,87}\mathrm{Rb}$ atoms at above-Doppler temperatures, we show simultaneous cooling of both species down to the Doppler temperature using two counter-propagating ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized beams from the frequency comb. The results indicate that simultaneous dual-species frequency comb cooling does not affect the cooling characteristics of individual atomic species. The results of this work imply that several atomic species could be cooled simultaneously using a single frequency comb source. This comb-based multichannel laser cooling could bring significant advances in multispecies atom interferometers for space applications and in the study of multispecies interactions.

We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment consists of their frequency degrees of freedom. By exploiting initially correlated frequency distributions and initial frequency-dependent phase factors, we are able to control all the four decoherence functions for polarization—corresponding to different open-system subspace divisions—almost independently of each other. Hence, our results demonstrate how, in a multipartite dephasing system, Markovian and non-Markovian dynamics can be arbitrarily divided between the subsystems, giving rise to the concept of memory partitions. We also discuss further implications the results have, e.g., on the dynamics of purity and entropy within the two-qubit system.

Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamiltonian and a dissipator of the Lindblad form in an enlarged Hilbert space, we show that spontaneous collapse can induce the decay dynamics in both quantum state and master equations. Moreover, we show that the decay property of a flavor-oscillating system is intimately connected to the time (a)symmetry of the noise field underlying the collapse mechanism. This (a)symmetry, in turn, is related to the definition of the stochastic integral and can provide a physical intuition behind the Itō-Stratonovich dilemma in stochastic calculus.

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv=\lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems $Av=\lambda Bv$, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm-Liouville problems. Another example comes from linear ideal magnetohydrodynamics, where phase estimation could be used to determine the stability of magnetically confined plasmas in fusion reactors.